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CORR
2008
Springer

Effective Complexity and its Relation to Logical Depth

8 years 2 months ago
Effective Complexity and its Relation to Logical Depth
Abstract--Effective complexity measures the information content of the regularities of an object. It has been introduced by M. Gell-Mann and S. Lloyd to avoid some of the disadvantages of Kolmogorov complexity, also known as algorithmic information content. In this paper, we give a precise formal definition of effective complexity and rigorous proofs of its basic properties. In particular, we show that incompressible binary strings are effectively simple, and we prove the existence of strings that have effective complexity close to their lengths. Furthermore, we show that effective complexity is related to Bennett's logical depth: If the effective complexity of a string x exceeds a certain explicit threshold then that string must have astronomically large depth; otherwise, the depth can be arbitrarily small.
Nihat Ay, Markus Mueller, Arleta Szkola
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Nihat Ay, Markus Mueller, Arleta Szkola
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